Simplify the following expression: $q = \dfrac{t^2 + 5t - 6}{t + 6} $
Solution: First factor the polynomial in the numerator. $ t^2 + 5t - 6 = (t + 6)(t - 1) $ So we can rewrite the expression as: $q = \dfrac{(t + 6)(t - 1)}{t + 6} $ We can divide the numerator and denominator by $(t + 6)$ on condition that $t \neq -6$ Therefore $q = t - 1; t \neq -6$